Constructing Long/Short Portfolios with the Omega ratio

We construct portfolios with an alternative selection criterion, the Omega function, which can be expressed as the ratio of two partial moments of the returns distribution. Finding Omega-optimal portfolios, in particular under realistic constraints like cardinality restrictions, requires to solve non-convex optimisation problems. Since standard (gradient-based) optimisation methods fail here, we suggest to use a heuristic technique (Threshold Accepting). The main purpose of the paper is to investigate the empirical performance of the selected portfolios, especially the effects of allowing short positions. Many studies on portfolio optimisation assume that short sales are not allowed. This is despite the fact that theoretically, short positions can improve the risk-return characteristics of a portfolio, and practically, institutional investors can and do sell stocks short.We investigate whether removing the non-negativity constraint really improves out-of-sample portfolio performance under realistic assumptions, that is when optimal weights need to be estimated from the data, different transaction costs apply to long and short positions or short selling is restricted to specific assets.